This article is cited in 6 papers

An inductive approach to representations of complex reflection groups $G(m,1,n)$

O. V. Ogievetskii^ab, L. Poulain d'Andecy<sup>a

a</sup> Centre de Physique Théorique Campus de Luminy, Marseille, France
^b Lebedev Physical Institute, RAS, Moscow, Russia

Abstract: We propose an inductive approach to the representation theory of the chain of complex reflection groups $G(m,1,n)$. We obtain the Jucys–Murphy elements of $G(m,1,n)$ from the Jucys–Murphy elements of the cyclotomic Hecke algebra and study their common spectrum using representations of a degenerate cyclotomic affine Hecke algebra. We construct representations of $G(m,1,n)$ using a new associative algebra whose underlying vector space is the tensor product of the group ring $\mathbb{C}G(m,1,n)$ with a free associative algebra generated by the standard $m$-tableaux.

Keywords: group tower, Hecke algebra, reflection group, maximal commutative subalgebra, Young diagram, Young tableau.

Received: 04.04.2012

DOI: 10.4213/tmf8343

 English version: Theoretical and Mathematical Physics, 2013, 174:1, 95–108

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